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A194390 Numbers n such that sum{<1/2+k*r>-<k*r> : 1<=k<=n}=0, where r=sqrt(12) and < > denotes fractional part. 3
2, 4, 6, 8, 10, 12, 28, 30, 32, 34, 36, 38, 40, 56, 58, 60, 62, 64, 66, 68, 84, 86, 88, 90, 92, 94, 96, 112, 114, 116, 118, 120, 122, 124, 140, 142, 144, 146, 148, 150, 152, 168, 170, 172, 174, 176, 178, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every term is even; see A194368.

LINKS

Table of n, a(n) for n=1..48.

MATHEMATICA

r = Sqrt[12]; c = 1/2;

x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];

Flatten[Position[t1, 1]]  (* empty *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t2, 1]]       (* A194390 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];

Flatten[Position[t3, 1]]       (* A194391 *)

CROSSREFS

Cf. A194368.

Sequence in context: A309716 A198186 A264984 * A187688 A085884 A246404

Adjacent sequences:  A194387 A194388 A194389 * A194391 A194392 A194393

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)